ON QUASI-CLASS A OPERATORS

Abstract

Let QA denote the class of bounded linear Hilbert space operators T which satisfy the operator inequality

T^* |T^2| T ≥ T^* |T|^2 T.

Let f be an analytic function defined on an open neighbourhood U of σ(T) such that f is non–constant on the connected components of U. We generalize a theorem of Sheth [10] to f(T) ∈ QA.